Arithmetic of Computers

Arithmetic of Computers

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Lesson 6

The Octal System

From eight to ten

Page 196

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Your answer :
By the power of 8 it is shown multiplying in the number.
In a decimal number, such as 13910, we do not show any powers of 10 explicitly. We understand (if the number does not involve a fraction) that the right-hand digit is the coefficient of 100, the next digit to the left is the coefficient of 101, and so on.
In the octal system, we use exactly the same principle. We ordinarily write only the coefficients, such as 2138, whenever the subscript 8 identifies the number as an octal number. Therefore we read the right-hand digit (3 in this case) as the coefficient of 80, the next digit to the left as the coefficient of 81, the next to the left as the coefficient of 82, and so on. So we use the position of the digit to tell which power of 8 the digit is the coefficient of:
2 1 3 2 (82) +  1 (81) +  3 (80) = 2138.
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Answer to Self-Test Question 2, Lesson 6 :
By its position in the number.

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